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Beliebt Rechnen >

integral of (sqrt(x^3)+\sqrt[3]{x^2})

Lösung

\int (x^{3} + 3 x^{2}) d x

Lösung

\frac{2}{5} x^{\frac{5}{2}} + \frac{3}{5} x^{\frac{5}{3}} + C

Schritte zur Lösung

\int x^{3} + 3 x^{2} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{3} d x + \int 3 x^{2} d x

\int x^{3} d x = \frac{2}{5} x^{\frac{5}{2}}

\int 3 x^{2} d x = \frac{3}{5} x^{\frac{5}{3}}

= \frac{2}{5} x^{\frac{5}{2}} + \frac{3}{5} x^{\frac{5}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} x^{\frac{5}{2}} + \frac{3}{5} x^{\frac{5}{3}} + C

Graph

Beliebte Beispiele

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\int \frac{( ln ( x ) ) ^{15}}{x} d x

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